Which of the following is a rational expression whose domain has a restriction of x≠−1 ?(1 point)
Responses
x√2x+2
Start Fraction Start Root x End Root over 2 x plus 2 End Fraction
x+1x3
Start Fraction x plus 1 over x cubed End Fraction
6x3+60x
Start Fraction 6 x cubed plus 60 over x End Fraction
x2+6x+56x+6
x2+6x+56x+6
The rational expression whose domain has a restriction of x ≠ -1 is:
Start Fraction x + 1 over x cubed End Fraction.
To determine which of the given expressions is a rational expression with a domain restriction of x ≠ -1, we need to identify the expression that does not have x = -1 as a possible value for the variable.
Let's go through each of the options:
1. x√(2x+2)
This expression includes a square root, which typically introduces a domain restriction. However, there is no x = -1 within the square root. So, this expression does not have a domain restriction of x ≠ -1.
2. (x+1)/x^3
This expression is a rational expression with a denominator of x^3. To find out if it has a domain restriction of x ≠ -1, we need to check if x = -1 would make the denominator equal to zero. Plugging in x = -1 into the denominator, we get: (-1)^3 = -1. Since the denominator does not become zero, this expression does not have a domain restriction of x ≠ -1.
3. (6x^3+60x)/x
This expression is also a rational expression with a denominator of x. If we check if x = -1 would make the denominator equal to zero, we get: (-1) = -1. This means that x = -1 would result in a zero denominator, indicating a domain restriction of x ≠ -1.
4. x^2+6x+56x+6
This expression is not a rational expression because it does not have a fraction with variables in the numerator or denominator.
From the given options, the rational expression with a domain restriction of x ≠ -1 is:
(6x^3+60x)/x